Abstract
In this paper we continue our study of the fourth-order transgression on hyperähler manifolds introduced in the previous paper. We give a local construction for the fourth-order transgression of the Chern character form of an arbitrary vector bundle supplied with a self-dual connection on a four-dimensional hyperkähler manifold. The construction is based on the harmonic twistor formalism. Remarkably, the resulted expression for the fourth-order transgression is given in terms of the determinant of the ∂ ̄ -operator defined on fibers of the twistor fibration.
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